Flux-Tunable Josephson Diode Effect in a Hybrid Four-Terminal Josephson Junction.

We investigate the direction-dependent switching current in a flux-tunable four-terminal Josephson junction defined in an InAs/Al two-dimensional heterostructure. The device exhibits the Josephson diode effect with switching currents that depend on the sign of the bias current. The superconducting diode efficiency, reaching a maximum of |η| ≈ 34%, is widely tunable─both in amplitude and sign─as a function of magnetic fluxes and gate voltages. Our observations are supported by a circuit model of three parallel Josephson junctions with nonsinusoidal current-phase relation. With respect to conventional Josephson interferometers, phase-tunable multiterminal Josephson junctions enable large diode efficiencies in structurally symmetric devices, where local magnetic fluxes generated on the chip break both time-reversal and spatial symmetries. Our work presents an approach for developing Josephson diodes with wide-range tunability that do not rely on exotic materials.

Microwave-induced conductance replicas in hybrid Josephson junctions without Floquet-Andreev states.

Light-matter coupling allows control and engineering of complex quantum states. Here we investigate a hybrid superconducting-semiconducting Josephson junction subject to microwave irradiation by means of tunnelling spectroscopy of the Andreev bound state spectrum and measurements of the current-phase relation. For increasing microwave power, discrete levels in the tunnelling conductance develop into a series of equally spaced replicas, while the current-phase relation changes amplitude and skewness, and develops dips. Quantitative analysis of our results indicates that conductance replicas originate from photon assisted tunnelling of quasiparticles into Andreev bound states through the tunnelling barrier. Despite strong qualitative similarities with proposed signatures of Floquet-Andreev states, our study rules out this scenario. The distortion of the current-phase relation is explained by the interaction of Andreev bound states with microwave photons, including a non-equilibrium Andreev bound state occupation. The techniques outlined here establish a baseline to study light-matter coupling in hybrid nanostructures and distinguish photon assisted tunnelling from Floquet-Andreev states in mesoscopic devices.

Phase-engineering the Andreev band structure of a three-terminal Josephson junction.

In hybrid Josephson junctions with three or more superconducting terminals coupled to a semiconducting region, Andreev bound states may form unconventional energy band structures, or Andreev matter, which are engineered by controlling superconducting phase differences. Here we report tunnelling spectroscopy measurements of three-terminal Josephson junctions realised in an InAs/Al heterostructure. The three terminals are connected to form two loops, enabling independent control over two phase differences and access to a synthetic Andreev band structure in the two-dimensional phase space. Our results demonstrate a phase-controlled Andreev molecule, originating from two discrete Andreev levels that spatially overlap and hybridise. Signatures of hybridisation are observed in the form of avoided crossings in the spectrum and band structure anisotropies in the phase space, all explained by a numerical model. Future extensions of this work could focus on addressing spin-resolved energy levels, ground state fermion parity transitions and Weyl bands in multiterminal geometries.

Zeeman- and Orbital-Driven Phase Shifts in Planar Josephson Junctions.

We perform supercurrent and tunneling spectroscopy measurements on gate-tunable InAs/Al Josephson junctions (JJs) in an in-plane magnetic field and report on phase shifts in the current-phase relation measured with respect to an absolute phase reference. The impact of orbital effects is investigated by studying multiple devices with different superconducting lead sizes. At low fields, we observe gate-dependent phase shifts of up to φ0 = 0.5π, which are consistent with a Zeeman field coupling to highly transmissive Andreev bound states via Rashba spin-orbit interaction. A distinct phase shift emerges at larger fields, concomitant with a switching current minimum and the closing and reopening of the superconducting gap. These signatures of an induced phase transition, which might resemble a topological transition, scale with the superconducting lead size, demonstrating the crucial role of orbital effects. Our results elucidate the interplay of Zeeman, spin-orbit, and orbital effects in InAs/Al JJs, giving improved understanding of phase transitions in hybrid JJs and their applications in quantum computing and superconducting electronics.

Demonstration of the Nonlocal Josephson Effect in Andreev Molecules.

We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current-phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.

Ubiquitous Superconducting Diode Effect in Superconductor Thin Films.

The macroscopic coherence in superconductors supports dissipationless supercurrents that could play a central role in emerging quantum technologies. Accomplishing unequal supercurrents in the forward and backward directions would enable unprecedented functionalities. This nonreciprocity of critical supercurrents is called the superconducting (SC) diode effect. We demonstrate the strong SC diode effect in conventional SC thin films, such as niobium and vanadium, employing external magnetic fields as small as 1 Oe. Interfacing the SC layer with a ferromagnetic semiconductor EuS, we further accomplish the nonvolatile SC diode effect reaching a giant efficiency of 65%. By careful control experiments and theoretical modeling, we demonstrate that the critical supercurrent nonreciprocity in SC thin films could be easily accomplished with asymmetrical vortex edge and surface barriers and the universal Meissner screening current governing the critical currents. Our engineering of the SC diode effect in simple systems opens the door for novel technologies while revealing the ubiquity of the Meissner screening effect induced SC diode effect in superconducting films, and it should be eliminated with great care in the search for exotic superconducting states harboring finite-momentum Cooper pairing.

Small Charging Energies and g-Factor Anisotropy in PbTe Quantum Dots.

PbTe is a semiconductor with promising properties for topological quantum computing applications. Here, we characterize electron quantum dots in PbTe nanowires selectively grown on InP. Charge stability diagrams at zero magnetic field reveal large even-odd spacing between Coulomb blockade peaks, charging energies below 140 µeV and Kondo peaks in odd Coulomb diamonds. We attribute the large even-odd spacing to the large dielectric constant and small effective electron mass of PbTe. By studying the Zeeman-induced level and Kondo splitting in finite magnetic fields, we extract the electron g-factor as a function of magnetic field direction. We find the g-factor tensor to be highly anisotropic with principal g-factors ranging from 0.9 to 22.4 and to depend on the electronic configuration of the devices. These results indicate strong Rashba spin-orbit interaction in our PbTe quantum dots.

Semiconductor Epitaxy in Superconducting Templates.

Integration of high-quality semiconductor-superconductor devices into scalable and complementary metal-oxide-semiconductor compatible architectures remains an outstanding challenge, currently hindering their practical implementation. Here, we demonstrate growth of InAs nanowires monolithically integrated on Si inside lateral cavities containing superconducting TiN elements. This technique allows growth of hybrid devices characterized by sharp semiconductor-superconductor interfaces and with alignment along arbitrary crystallographic directions. Electrical characterization at low temperature reveals proximity induced superconductivity in InAs via a transparent interface.

Evidence of topological superconductivity in planar Josephson junctions.

Majorana zero modes-quasiparticle states localized at the boundaries of topological superconductors-are expected to be ideal building blocks for fault-tolerant quantum computing1,2. Several observations of zero-bias conductance peaks measured by tunnelling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor-semiconductor nanowires3-8. On the other hand, two-dimensional systems offer the alternative approach of confining Majorana channels within planar Josephson junctions, in which the phase difference φ between the superconducting leads represents an additional tuning knob that is predicted to drive the system into the topological phase at lower magnetic fields than for a system without phase bias9,10. Here we report the observation of phase-dependent zero-bias conductance peaks measured by tunnelling spectroscopy at the end of Josephson junctions realized on a heterostructure consisting of aluminium on indium arsenide. Biasing the junction to φ ≈ π reduces the critical field at which the zero-bias peak appears, with respect to φ = 0. The phase and magnetic-field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. As well as providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures11 and are scalable to the complex geometries needed for topological quantum computing9,12,13.

Transport Studies of Epi-Al/InAs Two-Dimensional Electron Gas Systems for Required Building-Blocks in Topological Superconductor Networks.

One-dimensional (1D) electronic transport and induced superconductivity in semiconductor nanostructures are crucial ingredients to realize topological superconductivity. Our approach for topological superconductivity employs a two-dimensional electron gas (2DEG) formed by an InAs quantum well, cleanly interfaced with an epitaxial superconductor (epi-Al). This epi-Al/InAs quantum well heterostructure is advantageous for fabricating large-scale nanostructures consisting of multiple Majorana zero modes. Here, we demonstrate transport studies of building-blocks using a high-quality epi-Al/InAs 2DEG heterostructure, which could be put together to realize various proposed 1D nanowire-based nanostructures and 2DEG-based networks that could host multiple Majorana zero modes. The studies include (1) gate-defined quasi-1D channels in the InAs 2DEG and (2) quantum point contacts for tunneling spectroscopy, as well as induced superconductivity in (3) a ballistic Al-InAs 2DEG-Al Josephson junction. From 1D transport, systematic evolution of conductance plateaus in half-integer conductance quanta is observed with Landé g-factor of 17, indicating the strong spin-orbit coupling and high quality of the InAs 2DEG. The improved 2DEG quality leads to ballistic Josephson junctions with enhanced characteristic parameters such as Ic Rn and Iexc Rn, the product of superconducting critical current Ic (and excess current Iexc) and normal resistance Rn. Our results of electronic transport studies based on the 2D approach suggest that the epitaxial superconductor/2D semiconductor system with improved 2DEG quality is suitable for realizing large-scale nanostructures for quantum computing applications.

Giant Spin-Orbit Splitting in Inverted InAs/GaSb Double Quantum Wells.

Transport measurements in inverted InAs/GaSb quantum wells reveal a giant spin-orbit splitting of the energy bands close to the hybridization gap. The splitting results from the interplay of electron-hole mixing and spin-orbit coupling, and can exceed the hybridization gap. We experimentally investigate the band splitting as a function of top gate voltage for both electronlike and holelike states. Unlike conventional, noninverted two-dimensional electron gases, the Fermi energy in InAs/GaSb can cross a single spin-resolved band, resulting in full spin-orbit polarization. In the fully polarized regime we observe exotic transport phenomena such as quantum Hall plateaus evolving in e^{2}/h steps and a nontrivial Berry phase.

Scaling of Majorana Zero-Bias Conductance Peaks.

We report an experimental study of the scaling of zero-bias conductance peaks compatible with Majorana zero modes as a function of magnetic field, tunnel coupling, and temperature in one-dimensional structures fabricated from an epitaxial semiconductor-superconductor heterostructure. Results are consistent with theory, including a peak conductance that is proportional to tunnel coupling, saturates at 2e^{2}/h, decreases as expected with field-dependent gap, and collapses onto a simple scaling function in the dimensionless ratio of temperature and tunnel coupling.

Quantized Conductance and Large g-Factor Anisotropy in InSb Quantum Point Contacts.

Because of a strong spin-orbit interaction and a large Landé g-factor, InSb plays an important role in research on Majorana fermions. To further explore novel properties of Majorana fermions, hybrid devices based on quantum wells are conceived as an alternative approach to nanowires. In this work, we report a pronounced conductance quantization of quantum point contact devices in InSb/InAlSb quantum wells. Using a rotating magnetic field, we observe a large in-plane (|g1| = 26) and out-of-plane (|g1| = 52) g-factor anisotropy. Additionally, we investigate crossings of subbands with opposite spins and extract the electron effective mass from magnetic depopulation of one-dimensional subbands.

Decoupling Edge Versus Bulk Conductance in the Trivial Regime of an InAs/GaSb Double Quantum Well Using Corbino Ring Geometry.

A Corbino ring geometry is utilized to analyze edge and bulk conductance of InAs/GaSb quantum well structures. We show that edge conductance exists in the trivial regime of this theoretically predicted topological system with a temperature-insensitive linear resistivity per unit length in the range of 2 kΩ/µm. A resistor network model of the device is developed to decouple the edge conductance from the bulk conductance, providing a quantitative technique to further investigate the nature of this trivial edge conductance, conclusively identified here as being of n type.

Generation and Detection of Spin Currents in Semiconductor Nanostructures with Strong Spin-Orbit Interaction.

Storing, transmitting, and manipulating information using the electron spin resides at the heart of spintronics. Fundamental for future spintronics applications is the ability to control spin currents in solid state systems. Among the different platforms proposed so far, semiconductors with strong spin-orbit interaction are especially attractive as they promise fast and scalable spin control with all-electrical protocols. Here we demonstrate both the generation and measurement of pure spin currents in semiconductor nanostructures. Generation is purely electrical and mediated by the spin dynamics in materials with a strong spin-orbit field. Measurement is accomplished using a spin-to-charge conversion technique, based on the magnetic field symmetry of easily measurable electrical quantities. Calibrating the spin-to-charge conversion via the conductance of a quantum point contact, we quantitatively measure the mesoscopic spin Hall effect in a multiterminal GaAs dot. We report spin currents of 174 pA, corresponding to a spin Hall angle of 34%.

Characterization of spin-orbit interactions of GaAs heavy holes using a quantum point contact.

We present transport experiments performed in high-quality quantum point contacts embedded in a GaAs two-dimensional hole gas. The strong spin-orbit interaction results in peculiar transport phenomena, including the previously observed anisotropic Zeeman splitting and level-dependent effective g factors. Here we find additional effects, namely, the crossing and the anticrossing of spin-split levels depending on subband index and magnetic field direction. Our experimental observations are reconciled in a heavy-hole effective spin-orbit Hamiltonian where cubic- and quadratic-in-momentum terms appear. The spin-orbit components, being of great importance for quantum computing applications, are characterized in terms of magnitude and spin structure. In light of our results, we explain the level-dependent effective g factor in an in-plane field. Through a tilted magnetic field analysis, we show that the quantum point contact out-of-plane g factor saturates around the predicted 7.2 bulk value.

Insulating state and giant nonlocal response in an InAs/GaSb quantum well in the quantum Hall regime.

We present transport measurements performed in InAs/GaSb double quantum wells. At the electron-hole crossover tuned by a gate voltage, a strong increase in the longitudinal resistivity is observed with increasing perpendicular magnetic field. Concomitantly with a local resistance exceeding the resistance quantum by an order of magnitude, we find a pronounced nonlocal resistance signal of almost similar magnitude. The coexistence of these two effects is reconciled in a model of counterpropagating and dissipative quantum Hall edge channels providing backscattering, shorted by a residual bulk conductivity.